The idea is of a creature made of rock. It is able to blend in with surrounding rocks. It eats rocks even though it doesn't have to, but nonetheless it is a treat given to it by the Foundation for good behavior. It is friendly and dog-like to summarize. By the way, it poops pebbles. I was considering it having an organic anatomy internally by the way.

The goal of the article is to be more adorable than narrative driven. Do you think it is possible with this idea?

I think the Rock Dragon should be rebranded as the Earth Dragon. I mean unless you plan to have it flying anomalously? I also think a specialised group could be involved that breed and protect the rock dragons? Which they've bred into their current docile form. Maybe explaining that they used to be bred by Chinese Emperors, to wage war. Their size allows them to be ridden like horses. There could be populations of wild rock dragons that are hidden and captive examples kept by Foundation. You could even do something similar to SCP-3209 with the current organisation allowed to continue their work, with Foundation watching out for wild specimens that end up outside of containment.

For this version, Rock Dragons are either small stone statues of dragons, sold as pets. They could freeze up like gargoyles when someone new is in sight, until they are introduced, which will reanimate them.

Or they are an anomalous rock dragon animal that is sold as a pet. The dragon will consume rocks offered obviously, and maybe between the rocky formations on its body it glows specific colours to show its mood?

I should clarify that the skip has no wings or any ability to fly and is called a dragon for being reptile-like but more like a salamander or a komodo dragon. Anyway, in regards to your suggestions.

I felt I could have this be a unique instance. I do like the idea of an emperor being involved. Could have a back story that it was an ancient experiment to create dangerous war beast but the outcome was not what they expected.

I could imagine it stopping and acting like a normal big rock when seeing someone it does not know. It makes it cuter.